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for what value of k will the set of planes intersect in a line? x+2y-z=0 x+9y-5z=0 K x-y+z=0

for what value of k will the set of planes intersect in a line?


 


x+2y-z=0


x+9y-5z=0


Kx-y+z=0

Grade:

1 Answers

mounika gajawada
31 Points
10 years ago

for three planes to  intersect on a line they gotta have infinite solutions

→ Δ=0 i.e; det of coefficients of planes is 0

→ 1*(9-5)-2*(1+5k)-1(-1-9k)=0

→ k=3

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